The frame of a bicycle, as shown in FIG. 1, is generally comprised of a top tube, a town tube, a seat tube and two seat stays respectively connected by a front frame tube connector, a rear frame tube connector and a bottom frame tube connector. When assembled, the top, down and seat tubes and the seat stays are respectively welded to the frame tube connectors to ensure the connections. This welding process applicable only when the tubes and seat stays of the frame and the frame tube connectors are all made from iron. In recent years, titanium and aluminum alloys have been intensively used for making bicycle frames and frame tube connectors. Because welding one bicycle frame tube of titanium alloy to another or to a frame tube connector of titanium alloy will damage the structural strength of the bicycle frame, welding process is not applicable in this case. Therefore, screw joints or adhesive devices may be used instead of welding process. FIG. 2 illustrates two frame tubes fastened to two lugs on a frame tube connector by screw joints according to the prior art. However, because one frame tube connector may receive two frame tubes, it is not easy to connect several frame tubes to a plurality of frame tube connectors by screw joints. FIG. 3 shows a frame tube connecting method which connects a frame tube to a lug on a frame tube connector by an adhesive device. According to this connecting method, the inside surface of the lug and the outside surface of the frame tube are respectively coated with a layer of bonding resin. After the coating of the bonding resin, the frame tube is inserted into the lug and becomes firmly retained in place as the bonding resin is hardened. However, the bonding resin may brittle easily after long uses, thereby causing the connection to become loosened.
FIG. 4 shows another frame tube connecting method which is to make an inside step on the inside surface of the lug and an outside step on the outside surface of the frame tube, and then to insert the frame tube into the lug permitting the steps to be engaged with each other. This method is critical in precision, therefore an expensive precision apparatus must be used for making the steps. If the steps are not precisely made at respective locations, the connection of the lug and the frame tube will be unstable. Therefore, this method cannot eliminate the problem of a high defective rate. If the frame tubes of a bicycle frame are not firmly connected together, the bicycle will be broken easily when it is moving over an uneven road at a high speed.